<h3><u>Question:</u></h3>
A ball is thrown into the air with an initial velocity of 22 meters per second.
The quadratic function h(t) = -4.9t2 + 22t + 5.5 represents the height of
the ball above the ground, in meters, with respect to time t, in seconds.
Determine h(3) and explain what it represents.
<h3><u>Answer:</u></h3>
h(3) = 27.4
h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.
<h3><u>Solution:</u></h3>
The quadratic equation that represents the height of the ball above the ground, h(t), in meters, with respect to time, t, in seconds is given by:
![h(t) = -4.9t^2+22t+5.5](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-4.9t%5E2%2B22t%2B5.5)
To find h(3), substitute t = 3 into given quadratic equation and solve for it
Plug in t = 3 in h(t)
![h(3) = -4.9(3)^2+22(3)+5.5\\\\\text{Simplify the above expression }\\\\h(3) = -4.9 \times 9 + 66 + 5.5\\\\h(3) = -44.1+66+5.5\\\\h(3) = 27.4](https://tex.z-dn.net/?f=h%283%29%20%3D%20-4.9%283%29%5E2%2B22%283%29%2B5.5%5C%5C%5C%5C%5Ctext%7BSimplify%20the%20above%20expression%20%7D%5C%5C%5C%5Ch%283%29%20%3D%20-4.9%20%5Ctimes%209%20%2B%2066%20%2B%205.5%5C%5C%5C%5Ch%283%29%20%3D%20-44.1%2B66%2B5.5%5C%5C%5C%5Ch%283%29%20%3D%2027.4)
Thus h(3) = 27.4
h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.